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Bravais Lattice refers to the three-dimensional configurations of arrangement of atoms in crystals. There are 14 Bravais Lattices which can be divided into 7 lattice systems. The term Bravais Lattice is named after Auguste Bravais, a French physicist. The concept of Bravais Law and Bravais Lattice was developed by Auguste Bravais.
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Key Terms: Crystal Lattice, Solids, Lattice Systems, Unit cell, Atoms, Crystal, Amorphous solids, Crystalline solids, Molecules, Ions
Amorphous and Crystalline solids
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Solids can be categorized into two types: Amorphous solids and crystalline solids. This classification is done on the basis of the arrangement of particles in the solid.
Crystalline solids have a definite geometrical shape. They follow the long range order in the arrangement of constituent particles such as atoms, ions, or molecules. Crystalline solids are true solids and they are anisotropic in nature.
Crystalline solids have a sharp melting point. Some examples of crystalline solids are quartz, calcite, and sodium chloride.
Crystalline Solids
Amorphous solids have an irregular shape. They follow the short range order in the arrangement of constituent particles. Amorphous solids are referred to as super cooled solids or pseudo solids. They are isotropic in nature.
Amorphous solids can be softened easily and molded into a variety of shapes. Some examples of amorphous solids are rubber, plastic, wax, and fused silica.
Amorphous Solids
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Bravais Lattice
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The geometric arrangement of points in a crystal where constituent particles like atoms, ions, or molecules occur is called a lattice. In other words, lattice points are points in a crystal where the possibility of finding a particle is highest. The lattice points are identical to each other.
A Bravais lattice is an array of discrete points with an arrangement and orientation that look exactly the same from any of the discrete points. The lattice points are indistinguishable from one another.
Types of Bravais Lattice
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There are 14 Bravais Lattices which can be divided into 7 lattice crystal systems. These are:
- Cubic System
- Tetragonal System
- Orthorhombic System
- Hexagonal System
- Rhombohedral or Trigonal System
- Monoclinic System
Lattice Systems
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1. Cubic System
There are three Bravais Lattices under the cubic system. All sides in cubic lattices are of the same length and the angle between all the faces is 90°. The three possible variations of cubic lattices are:
- Primitive or Simple Cubic Structure
An example of primitive cubic structure is Polonium.
- Body-Centered Cubic Structure
Some examples of body-centered cubic structures are iron, beta titanium, and chromium.
- Face-Centered Cubic Structure
Examples of face-centered cubic structure are nickel, aluminum, copper, and silver.
2. Tetragonal System
In a tetragonal system, two sides have the same length, and the third side has a different length. The angle between all the faces is 90°. There are two possible variations of tetragonal lattices:
- Primitive Tetragonal Structure
An example of primitive tetragonal structure is stannic oxide.
- Body-Centered tetragonal Structure
Titanium dioxide is an example of a body-centered tetragonal structure.
3. Orthorhombic System
There are four Bravais Lattices under the orthorhombic system. In an orthorhombic structure, all the sides are unequal. However, the angle between all the faces is the same i.e. 90°. The two possible variations under orthorhombic lattices are:
- Primitive Orthorhombic Structure
An example of primitive orthorhombic structure is rhombic sulphur.
- Body-Centered Orthorhombic Structure
Potassium nitrate is an example of body-centered orthorhombic structure.
- Face-Centered Orthorhombic Structure
An example of face-centered orthorhombic structure is barium sulfate.
- End-Centered Orthorhombic Structure
An example of end-centered orthorhombic structure is Magnesium sulfate heptahydrate.
4. Hexagonal System
There is only one Bravais Lattice under the hexagonal system: Primitive Hexagonal Structure. In this hexagonal structure, two sides are equal and one side is of a different length. Two faces have an angle of 90° and one face has an angle of 120°. Some examples of hexagonal structures are graphite, zinc oxide, and cadmium sulfide.
5. Rhombohedral or Trigonal System
There is only one Bravais Lattice under the rhombohedral system: Primitive Rhombohedral Cells. In a rhombohedral structure, all the sides are of equal length. However, two faces have an angle less than 90°. Some examples of rhombohedral structures are calcite and mercuric sulfide.
6. Monoclinic System
In a monoclinic structure, all the sides are unequal in length. One face has an angle of more than 90° and one face has an angle less than 90°. The two possible variations of monoclinic lattices are:
- Primitive Monoclinic Cells
Monoclinic sulphur is an example of primitive monoclinic structure.
- End-Centered Monoclinic Cells
An example of end-centered monoclinic structure is sodium sulfate decahydrate.
7. Triclinic System
There is only one Bravais Lattice under the triclinic system: Primitive Triclinic Cells.
In a triclinic structure, all the sides are unequal to each other in length and no angle is equal to 90o. Some examples of triclinic structures are potassium dichromate and boric acid.
Things to Remember
- Solids can be categorized into two types: amorphous solids and crystalline solids.
- Bravais Lattice refers to the arrangement of atoms into three-dimensional configurations in crystals.
- There are 14 Bravais Lattices which can be divided into 7 lattice systems.
- The geometric arrangement of points in a crystal where constituent particles like atoms, ions, or molecules occur is called a lattice.
- The seven lattice crystal systems are cubic system, tetragonal system, orthorhombic system, hexagonal system, rhombohedral system, monoclinic system, and triclinic system.
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Sample Questions
Ques: What is a unit cell? (1 Mark)
Ans: A unit cell is the smallest repeating unit of a crystal lattice. The Unit cell is the foundation of the crystal.
Ques: What are the characteristics of crystal lattice? (1 Mark)
Ans: In a crystal lattice, the points are known as lattice points and each point represents either an atom, ion, or molecule. Crystal lattices have a geometrical shape.
Ques: What is the importance of a lattice point? (1 Mark)
Ans: A lattice point indicates the position of a constituent particle such as ion, molecule, or atom. This positioning of lattice points is responsible for the shape of the crystalline solids.
Ques: What are the categories of unit cells? (2 Marks)
Ans: There are two categories of a unit cell: primitive unit cells and centered unit cells. In primitive unit cells, the particles are present at the corner of the unit cell. In centered unit cells, the particles are present at the corners as well as other positions.
Ques: What are cubic unit cells. Write some elements that have cubic unit cells? (2 Marks)
Ans: In a cubic unit cell, all sides are of the same length and the angle between all the faces is 90°. Some elements that have cubic unit cells are nickel, copper, chromium, iron, silver, beta titanium and polonium.
Ques: How can one distinguish between Hexagonal unit cell and cubic unit cell? (2 Marks)
Ans: In a cubic unit cell, all sides in cubic lattices are of the same length and the angle between all the faces is 90° whereas in a hexagonal unit cell, two sides are equal and one side is of a different length. Two faces have an angle of 90° and one face has an angle of 120°.
Ques: What are the different types of centered unit cells? (3 Marks)
Ans: There are three types of centered unit cells: Body-Centred Unit Cells, Face-Centred Unit Cells, and End-Centred Unit Cells.
- In body centered unit cells, the particles are at the corners and body centers.
- In face centered unit cells, the particles are at corners as well as the center of faces.
- In end centered unit cells, the particles are present at corners and at the opposite faces.
Ques: Explain the Tetragonal and Orthorhombic lattice crystal system. (3 Marks)
Ans: There are two Bravais Lattices under the tetragonal system. In a tetragonal structure, two sides have the same length, and the third side has a different length. The angle between all the faces is 90°. There are two possible variations of tetragonal lattices: Primitive Tetragonal Cells and Body-Centered tetragonal Cells. An example of primitive tetragonal structure is stannic oxide. An example of a body-centered tetragonal structure is titanium dioxide.
There are four Bravais Lattices under the orthorhombic system. In an orthorhombic structure, all the sides are unequal. However, the angle between all the faces is the same i.e. 90°. The two possible variations under orthorhombic lattices are: Primitive Orthorhombic Cells, Body-Centered Orthorhombic Cells, Face-Centered Orthorhombic Cells, and End-Centered Orthorhombic Cells. An example of primitive orthorhombic structure is rhombic sulphur. An example of body-centered orthorhombic structure is potassium nitrate. An example of face-centered orthorhombic structure is barium sulfate. An example of end-centered orthorhombic structure is Magnesium sulfate heptahydrate.
Ques: What is the difference between amorphous solids and crystalline solids? (3 Marks)
Ans: Crystalline solids have a definite geometrical shape whereas amorphous solids have an irregular shape. Crystalline solids follow long range order whereas amorphous solids follow short range order. Amorphous solids are isotropic in nature whereas crystalline solids are anisotropic in nature. Some examples of crystalline solids are calcite, quartz, and sodium chloride. Some examples of amorphous solids are plastic, wax, rubber, and fused silica.
Ques: Which are the lattice crystal systems with only one Bravais lattice? (5 Marks)
Ans: There are three lattice systems with only one Bravais lattice under them: Hexagonal system, Rhombohedral system, and Triclinic system.
There is only one Bravais Lattice under the hexagonal system: Primitive Hexagonal Cells. In this hexagonal structure, two sides are equal and one side is of a different length. Two faces have an angle of 90° and one face has an angle of 120°. Some examples of hexagonal structures are graphite, zinc oxide, and cadmium sulfide.
Triclinic system also has only one Bravais Lattice: Primitive Triclinic Cells. In a triclinic structure, all the sides are unequal to each other in length and no angle is equal to 90°. Some examples of triclinic structures are potassium dichromate and boric acid.
The Bravais Lattice under the rhombohedral system is Primitive Rhombohedral Cells. In a rhombohedral structure, all the sides are of equal length. However, two faces have an angle less than 90°. Some examples of rhombohedral structures are calcite and mercuric sulfide.
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